Forecasting real estate returns using financial spreads
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Accepted Version
Brooks, C. and Tsolacos, S. (2001) Forecasting real estate returns using financial spreads. Journal of Property Research, 18 (3). pp. 235-248. ISSN 1466-4453 doi: https://doi.org/10.1080/09599910110060037 Available at http://centaur.reading.ac.uk/35970/
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Forecasting Real Estate Returns using Financial Spreads
Chris Brooks (corresponding author), ISMA Centre, PO Box 242, The University of
Reading, Whiteknights, Reading RG6 6BA; e-mail: [email protected]
and
Sotiris Tsolacos, Jones Lang LaSalle, 22 Hanover Square, London, W1A 2BN
October 2000
Forecasting Real Estate Returns using Financial Spreads
Abstract
This paper examines the predictability of real estate asset returns using a number of time
series techniques. A vector autoregressive model, which incorporates financial spreads, is
able to improve upon the out of sample forecasting performance of univariate time series
models at a short forecasting horizon. However, as the forecasting horizon increases, the
explanatory power of such models is reduced, so that returns on real estate assets are best
forecast using the long term mean of the series. In the case of indirect property returns,
such short-term forecasts can be turned into a trading rule that can generate excess returns
over a buy-and-hold strategy gross of transactions costs, although none of the trading
rules we develop could cover the associated transactions costs. We therefore conclude
that such forecastability is entirely consistent with stock market efficiency.
J.E.L. Classifications: C32, C52
Keywords: real estate returns, spreads, forecasting, time series models, vector
autoregressions
The authors acknowledge comments from two anonymous referees on a previous version of the paper.
The usual disclaimer applies.
1
1. Introduction
There is considerable evidence in the real estate literature that the behaviour of real estate
returns, that is returns on real estate-backed assets, are related to economic trends and
changing business conditions, and that they can be modelled, at least in part, using
publicly available economic information (Chan et al, 1990; McCue and Kling, 1994 and
Ling and Naranjo, 1997). This information is contained in a number of well publicised
macroeconomic financial time-series used in financial markets. Two variables commonly
used in the existing literature as indicators of future economic and monetary conditions
are the term structure of interest rates and the gilt-equity ratio. Research in the area of real
estate return predictability has been extended to investigate the possibility of superior
investment performance of real estate portfolios utilising the predictive power of real
economy variables and of financial aggregates.
Since the large majority of these studies examine the predictability of real estate returns
in the context of the US, further research is warranted to provide empirical evidence on
the linkages between the macroeconomy and real estate returns in other markets. This
need is particularly pronounced in European markets where equity investors are
increasingly considering real estate backed stocks as an investment vehicle in their
portfolios (see Ball et al (1998) for the increasing importance of the indirect property
vehicles). Although all equities are valued according to the expected future profit stream
of the firms, it can be argued that the fundamentals underpinning these profit streams and
returns on real estate backed stocks may differ from those on other types of stocks,
resulting in distinct time series behaviour of returns between these asset classes. The
main reason for this feature is the fact that the former are expected to reflect conditions in
the underlying direct property market. This, coupled with the evidence that real estate
2
returns seem to be more predictable than returns on other assets (Liu and Mei, 1992),
makes it possible that investors might be able to exploit this predictability in order to
pursue more profitable investment strategies, or more efficient portfolio diversification in
the mean-variance sense than portfolios which exclude real estate as an asset class. In
addition, although previous studies have explained the historical variation in real estate
returns using a set of predetermined variables within pre-specified frameworks, such as
multifactor regression models and vector autoregressions, they have not tested for the
forecasting ability of the different methodologies and variables. Therefore, the question
that arises is how accurately the real estate return generating models in the existing
literature predict the direction in future values of real estate returns and how suitable they
are for the purpose of short-term and longer term forecasting.
The main thrust of the present study is to examine the performance of alternative
econometric methodologies in forecasting real estate returns in the short-run in the UK.
Real estate returns are defined as the growth rate in the Primark Datastream price index
of real estate stocks. An analyst can study the time series properties of past data on real
estate returns and utilise this information to make short term predictions. Alternatively,
these forecasts can be made based upon a more general modelling methodology of real
estate return determination which includes information contained in lagged
macroeconomic or financial variables. The particular aim of this research is to forecast
the short- and long-run variation in real estate returns utilising both the time series
properties of the returns series alone and then a multivariate model that incorporates the
term structure of interest rates and the gilt-equity yield ratio to exploit the economic
information content of these variables. It is very important that investors have evidence
on whether the time series properties of real estate returns can be used for forecasting
3
purposes or whether they should employ more general models and frameworks to carry
out the forecasting analysis. This study provides the first evidence on comparative
forecasting research work in the field of real estate returns in the UK based on four
different prediction methodologies. The study also evaluates whether the relative
forecasting accuracy of these methodologies is invariant as the forecasting horizon
becomes longer.
The remainder of the paper is organised in five sections. A discussion of the methodology
followed and data employed in this paper is presented in section 2. Section 3 reports the
empirical findings while section 4 presents a comparative analysis of the forecastability
of direct and indirect property returns. Section 5 offers a trading rule to exploit potential
forecastabilities in the indirect returns series, and finally, section 6 concludes.
2. Forecasting frameworks, data, and production of forecasts
The simplest approach to forecasting real estate returns is to utilise the time series
properties of the returns series itself. For this purpose, forecasts are derived from two
models: (i) a forecasting model that simply comprises the long term mean of the returns
series, estimated as the unconditional mean of a trailing sample (in this case of size 200
observations) and (ii) an ARMA model which is fitted to the property returns series, with
the optimal model order being chosen by Akaike’s information criterion, Schwarz’s
Bayesian criterion, and the Hannan-Quinn criterion.
An third approach to forecasting real estate returns is to consider additional explanatory
variables that explicitly incorporate analysts’ expectations about business conditions in a
vector autoregressive (VAR) model framework. The set of variables for inclusion in the
4
VAR is determined by the conclusions of recent research investigating the modelling of
stock returns or real estate returns. It is assumed that changing economic conditions are
ultimately responsible for the variation in property share prices. There is ample evidence
in applied economics research that the term structure of interest rates and the gilt-equity
yield ratio (GEYR) adjust when market participants revise their expectations about the
state of the economy. Therefore, they can be used as leading indicators of future business
conditions (Estrella and Hardouvelis, 1991; Hardouvelis, 1994; Davis and Fagan, 1997).
Several authors have argued that the term structure of interest rates contains information
about the future course of the economy (Campbell, 1987; Chen, 1991; Estrella and
Hardouvelis, 1991; Hardouvelis, 1994). In particular, Estrella and Hardouvelis (1991)
demonstrate that the yield curve has predictive power beyond that contained in the short
term interest rate, and can help predict changes in national output up to four periods
ahead. The term structure of interest rates is defined as the difference between the long-
term and the short-term rates of interest. This spread is usually positive so that the yield
curve is upward sloping. A tightening of monetary policy in order to kerb inflation or
inflationary growth will be reflected in higher short-term interest rates. If the financial
markets believe that future economic activity will slow down and therefore that the future
short-term rate of interest will fall, the yield curve will flatten out or even decline. High
short rates in the current period can lead to lower aggregate investment expenditure that
in turn results in a decline in future economic activity. Therefore, market participants
expect lower prices and returns on traded property assets during the forthcoming
economic contraction. Chan et al (1992) provide supporting evidence to the view that the
term structure affects real estate returns but Liu and Mei (1992) did not find such
5
evidence. On the other hand, Ling and Naranjo (1997) found that the spread variable
could become important in particular periods.
The predictive power of the gilt-equity yield ratio has not been examined in the literature
on real estate returns, although research on general equity market indices suggests that it
can have additional explanatory power beyond that contained in other macroeconomic or
financial variables (see Levin & Wright, 1999; Brooks and Persand, 2000). The GEYR
ratio is measured as the ratio of the long gilt yield to the equity dividend yield. Levin and
Wright argue that the GEYR has a normal “long run” level, reflecting a long run no-
arbitrage relation between government bond and equity markets. Movements in this ratio
are strongly affected by changes in the stock price and dividend yield (see Davis and
Fagan, 1997). If, due to higher expected profitability, the dividend yield falls, the GEYR
may become too high so that equities are thought expensive relative to bonds. Levin and
Wright also state that bond yields do not fall, the low value of equity yields cannot be
sustained. Therefore, equity prices, and in the context of the present study, the prices of
property stocks, must fall to restore the long run equilibrium. When the GEYR is too low,
equity prices are expected to rise in order to restore the equilibrium relationship.
Other macroeconomic variables, such as changes in unemployment, inflation, short term
interest rates are not included in the results given here for two reasons. First, the results
obtained by using these variables (not reported but available from the authors upon
request) were inferior to those reported here using the two financial variables. Second,
recent research by Brooks and Tsolacos (1999) has shown that the other variables do not
even have any in-sample predictive power for real estate returns, evidenced by the joint
6
lack of significance of the coefficients in the VAR representations when general stock
market effects are removed.
The data employed in this study comprise monthly observations on the Primark
Datastream UK Property Index, the term spread (measured as the difference between the
yields on a 20 year government bond and the three month Treasury bill rate), and the gilt-
equity yield ratio (calculated by taking the ratio of the yield on 20 year government bonds
and the dividend yield on the FTSE 100). All data were obtained from Datastream
International, and cover the period January 1968 until January 1998, yielding a total of
361 sample points. The property index employed comprises a market value-weighted
index constructed by Primark Datastream, based upon the top 26 property stocks traded
on the London Stock Exchange. The relative weightings given to the component stocks
are updated on a monthly basis.
Some summary statistics for the data are presented in table 1. The property returns series
shows significant autocorrelation at the first lag, but none thereafter, and is both skewed
and leptokurtic. Meanwhile, the GEYR series is leptokurtic but not skewed, and the
spread series seems to show little departure from normality. Both the GEYR and spread
series are very strongly autocorrelated, but there is no evidence that any of the series are
non-stationary.
The effect of the above variables is examined within the context of an unrestricted
reduced-form vector autoregressive (VAR) model, with three equations (one for each of
the three variables: real estate returns, the term structure, GEYR), which is described by:
Yt = 0 + 1Yt-1 + ... + mYt-m + ut (1)
7
where Y is the set (or 31 vector) of variables included in the system, the terms give the
sets of coefficient vectors (0 is a 31 vector of constants, 1 ,..., m are 33 matrices of
coefficients on the lagged variables, m represents the number of lags of each variable in
each equation), and ut is a vector of error terms (or innovations) which are assumed to be
mutually uncorrelated and independent of the Ys. The number of lags of each variable to
be included in the VAR is chosen using multivariate generalisations of Akaike’s
Schwarz’s Bayesian, and the Hannan-Quinn information criterion (see, for example,
Enders, 1995).
The forecasts are constructed as follows. The sample is split roughly in half, with the first
200 observations being used for in-sample model estimation. Then a series of out of
sample forecasts up to six steps ahead are generated. The sample is then rolled forward
by one observation, the models re-estimated, and a new series of forecasts constructed.
This procedure is repeated until 160 such forecasts are generated. The UK economy has
been the subject of numerous changes in monetary and fiscal policy over our 30 year
sample period (see below), and thus the use of shorter windows used in a rolling fashion
helps to minimise the possibilities of structural breaks whilst ensuring sufficient in-
sample data to estimate the models and to produce the forecasts.
The forecasts for the different models are evaluated and compared on the grounds of
mean squared error (MSE), mean absolute error (MAE) and the proportion of times that
the model correctly predicts the return’s sign. The “best” model is defined as the one with
the lowest mean squared or mean absolute error, since this would indicate the model
whose forecasts are closer to the realised values of the series, and whose forecasts are
therefore the most accurate. However, it has also been shown (Gerlow et al., 1993) that
8
the accuracy of forecasts according to traditional statistical criteria may give little guide
to the potential profitability of employing those forecasts in a market trading strategy, so
that models which perform poorly on statistical grounds may still yield a profit if used for
trading, and vice-versa. Models that can accurately forecast the sign of future returns, or
can predict turning points in a series have been found to be more profitable (Leitch and
Tanner, 1991). Hence the proportion of times that the model correctly predicts the sign of
the real estate return is also calculated.
In table 2, we present the results of Granger-causality tests for the three variables
employed in the analysis, used to determine whether the VAR formulation seems sensible
or not. A detailed description of the operation of this test and its interpretation can be
found in Brooks and Tsolacos (1999). Changes in the property index are found to be
caused by previous changes in its own values, and by previous changes in the values of
the GEYR and the interest rate spread. Meanwhile, changes in the property index do not
seem to Granger-cause changes in either of the other two series. Thus we conclude that
the other two variables are weakly exogenous, and that the additional information
contained in the GEYR and the term spread could be useful for modelling and forecasting
changes in the property index.
3. Results
Initially the order of the ARMA and the VAR models was established as accomplished
by the three information criteria. The in-sample minimisation of Akaike’s criterion
suggested that four lags of the autoregressive part and two lags of the moving average
term should be used, while the other two criteria both favoured an ARMA(1,1) model.
For the VAR model the same criteria indicated the inclusion of four lags, one lag and one
9
lag respectively. We employ the same number of lags for each variable so that the VAR
is completely unrestricted. The results for the out of sample forecasts generated using the
different methods, with ARMA and VAR models being estimated using the numbers of
lags suggested by all the criteria, are given in Table 3 for 1 and 6 month prediction
horizons.
In this application, the forecast accuracy evaluation measures give differing orderings of
models. The VAR models, which attempt to incorporate the macroeconomic influences
of the term spread and the gilt-equity yield ratio, give surprisingly poor overall
performances for a forecasting horizon of one or six steps ahead, on MSE or MAE
grounds. When evaluated using these criteria, the VAR(4) does particularly badly, and
presumably represents an over-parameterisation, given that there are 12 right-hand side
variables plus a constant, in each equation. The VAR(1), on the other hand, whilst not the
best model, produces 1-step ahead forecasts which are among the most accurate. Even the
small VAR model rapidly loses forecasting power, however, as the forecast horizon is
extended. This is not surprising, since to produce multi-step ahead forecasts from a VAR,
the values of the other variables in the system must also be forecasted (within the
system), which introduces another source of uncertainty and potential error. In order to
further evaluate why the VAR model (which contains all of the information in the
univariate autoregressive framework, plus additional variables) did not produce superior
forecasts compared with simpler models, we compute and plot in Figures 1 to 3 the
impulse-response functions associated with unit shocks in each of the three explanatory
variables, which are subsequently tracked for 24 months. Considering the signs of the
responses, changes in the value of the property index are positively correlated over a
short horizon, since the impulse response is large positive for lags 1 and 2, but the
10
impulse-responses thereafter are negative, although the two standard error bands (the
dotted lines) span the horizontal axis, indicating that the impulse-response coefficients
are no longer significant. The response of the property index to changes in the GEYR, in
Figure 2, shows no clear pattern over time. The unit shock of GEYR leads first to a rise,
then a fall, and then a rise in the value of the property index, although overall the effect is
positive. Similarly for changes in the term spread, the effect upon the real estate index is
difficult to determine, with first a fall, and then a rise, and then a fall in the value of the
index following a unit shock. For all three plots, however, it is clear that after perhaps 5
or 6 periods, the effects of the shocks for the current value of the property index returns,
are negligible.
The best models, for short-term forecasts are the long term mean on MSE grounds, and
the profligate ARMA(4,2) on MAE grounds, while the VAR(4) produces the highest
proportion of correct sign predictions. For the 6-month ahead forecasts, the long term
mean produces the most accurate forecasts under all evaluation measures.
4. The Forecastability of Direct Versus Indirect Property Investment Returns
In this section, we compare the relative forecast accuracies of the various models
presented above using the returns on both the indirect property investment vehicle (the
equity quoted property index) and the returns on a direct property investment index - the
IPD monthly total return series. The latter is compiled from valuation and management
records for individual buildings in complete portfolios. The IPD total return is defined as
the overall return on capital employed and is the sum of income return and capital
growth. The Income return is income receivable net of management and irrecoverable
costs divided by capital employed through the month. Capital growth is the change in
11
capital value from one valuation to the next, net of any capital flows, divided by capital
employed (more information can be found in the IPD UK monthly index publications).
Since the IPD series is only available from December 1986, we also re-compute the
forecasts for the indirect property series analysed above for the same sample periods in
order to facilitate comparisons. Thus forecasts are now generated using a moving window
of 5 years’ (60 months’) worth of data, with forecasts up to 6 steps ahead being generated
and then the sample rolled forward 1 observation until 74 such forecasts are produced.
The results are presented in tables 4 and 5.
Again, model orders are chosen using Akaike’s, Schwarz’s Bayesian, and the Hannan-
Quinn information criteria. These criteria chose for indirect property series, and for the
ARMA models, a (2,5) - all criteria; for the direct (IPD) series the selected models were
(6,3) - AIC, (3,4) - SBIC and HQIC. All three criteria chose a VAR(1) for the indirect
series, while AIC chose a VAR(2), but SBIC and HQIC chose a VAR(1) for the direct
series. The fact that the selected lag-lengths and sizes of models are larger for the direct
property returns is indicative that there is potentially more forecastable structure in this
series than that based on equities.
The results in table 4 are broadly similar to those in table 3, although there are some
differences due to the change in sample length and the timing of the estimation and
forecasts. In table 4, the VAR model for the indirect returns is almost universally
superior. It provides the lowest MSE and MAE, and the highest proportion of correct sign
predictions, except at the longest forecasting horizon, where the VAR is the worst model
for sign prediction, getting only half of the 6-step ahead signs right.
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Table 5 presents the results for the appraisal-based IPD series. In this case, it is clearly the
ARMA approach, based upon only lags of the property returns themselves, which is the
winner, while the VAR model, containing additional information regarding the financial
markets, provides the least accurate forecasts, except in terms of sign predictions. The
parsimonious VAR(1) model provides a marginally higher proportion of correct sign
predictions at the short forecasting horizon, although the ARMA(1,1) and ARMA(1,3)
models are better as the prediction horizon increases.
In general, we can state that the use of “generous” information criteria, such as Akaike’s,
will lead to the selection of models which are over-parameterised, leading to poor
forecasts. Those concerned with forecasting real estate returns should be concerned to use
small models which do not use up valuable degrees of freedom, and which can
generalise.
It seems also that there is a great deal more forecastability in the appraisal-based, as
opposed to the equity-based series. This is evidenced by the fact that some models are
able to correctly predict the direction of change of the former series up to 6 months ahead
with over 90% accuracy. In financial markets, this accuracy would be considered
phenomenal. The mean absolute and mean squared errors of the time series and VAR
models are still smaller than those based on the long term mean, even at the 6 months
ahead horizon. This is, however, hardly surprising, and the apparent predictability of the
direct returns could be merely a statistical artefact, resulting from appraiser-induced
smoothness of the series. This smoothness in the series is exacerbated by the frequency of
the valuations. Monthly valuations of commercial properties do not provide sufficient
time for economic and other information to induce a significant variation in total returns.
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Therefore, current returns are bound to be linked to previous returns since they are not
traded at the frequency of the property shares. On the other hand, this long memory in
direct property returns may reflect characteristics of the property market that result in
cyclical shocks having long-term effects on rental and capital values.
4. Production and testing of trading rules
Although the evidence for the apparent predictability of property returns, both direct and
indirect, may be considered prima facie evidence of stock market informational
inefficiency. However, according to modern definitions of stock market efficiency, a
market may only be considered inefficient with respect to a particular information set if it
is possible to make abnormal profits from trading on the basis of that information set. In
order to investigate whether we can find any evidence of property market informational
inefficiency, we develop a set of trading rules based on the forecasts produced as
discussed above. For the reasons outlined above, the trading rules are developed only in
the context of indirect, equity-based property returns. The results of a trading rule based
on appraisal-based returns are likely to be misleading and unrealistic since such returns
are not based on transactions data, and therefore it may not in fact have been possible to
buy or sell property at the prevailing valuation prices. Additionally, investing in direct
property is likely to occur large transactions costs and market orders to buy or sell direct
property will only be executed with a long lag.
Although there are an infinite number of ways to operationalise a trading rule, we
consider a simple approach where an investor is either long the equity-based property
index or has no position, with the funds being held in treasury bills and therefore earning
the short term “risk-free” rate of interest. The 1-step and 6-step ahead forecasts are
14
produced, and a decision about whether to be in property is made on that basis. We
employ two rules: first, invest in the property stock index if the property return during the
next period is forecast to be positive; second, invest in property only if the return forecast
for the next month is greater than the average return over the sample period (i.e. greater
than 0.87% per month). In each case, if a return is predicted to be sufficiently large to
signal a buy, the property index notionally purchased. Then, the sample is rolled forward
one observation, and if the next return predicted positive again, the index continues to be
held, and so on. If the return is then predicted to be negative, however, the index is sold,
with the proceeds invested in the risk free rate. It is assumed that the investment began at
the start of our out of sample period and continued for the full 160 observations (i.e. a 13
years and 4 month period). We can effectively ignore risk in these calculations, since the
benchmark will be a “buy-and-hold the property index” approach, and this is likely to
represent more risk than our trading strategies, which involve being out of equities and in
treasury bills for part of the period.
Table 6 presents the trading profitability results, denominated in simple annualised
percentage returns, for each of the 5 models. The long-term mean model produces
property return forecasts that are always (small and) positive. Therefore, the long term
mean rule would be identical to passively holding the property index throughout the
whole period. The simple average annualised return to simply holding the property index
throughout is 8.07%. Overall, some of the models are able to modestly improve on this
profitability. The best performing models in aggregate are the VAR models, which
produce returns in excess of 9% per annum for the 1 step ahead forecasts with holdings in
equities being based on any positive forecasted returns. In general, as one might have
anticipated, trading on the basis of the 1-step ahead forecasts is more profitable than
15
trading on the basis of the 6-step ahead forecasts. Such a result ties in with the statistical
evaluation, which showed that the one step ahead forecasts are typically more accurate
and give a higher percentage of correct sign predictions.
A further cautionary note is required, however, in interpreting these results. The returns
presented in table 6 are calculated gross of transactions costs. Sutcliffe (1997) suggests
that an appropriate “round-trip” figure for transacting in companies contained in the
FTSE-100 is 1.7% of the value of the purchase/sale per transaction for an investor. This
figure is made up of bid /ask spread (0.8%), stamp duty (0.5%) and commission (0.4%).
Even ignoring the fact that some of the companies in the property index are not in the
FTSE 100, and are therefore likely to be less liquid with higher spreads, these
transactions costs are likely to wipe out any profits made by the trading rules. The best
performing rule generates a return of 9.26% per annum, but would generate
approximately 3-4 trades per year, resulting in transactions costs of around 6% per
annum. A filter which states that investors should only buy into the property index when
the index is predicted to rise by more than its historical average, typically results in fewer
trades, but also generates lower gross returns. For example, the best performing model in
the context of the strict filter is the VAR(1) using one-step ahead predictions, giving an
average annual return of 8.70%. This rule still requires 37 trades over the out of sample
period (approximately 2-3 trades per year), again wiping out any excess gross
profitability over a pure buy-and-hold equities strategy. Under modern definitions of
market efficiency, forecastability in returns can only be considered evidence for market
informational inefficiency if those forecasts can be turned into a trading rule that
generates abnormal returns net of costs. Since our trading rules could not generate excess
returns net of transactions costs, we would infer that the apparent forecastability of
16
indirect property returns is entirely consistent with stock market efficiency and the
absence of possibilities for arbitrage.
6. Conclusions
The present study examined the performance of three different forecasting techniques that
are available to analysts and investors to forecast real estate returns in the UK. Two of
these techniques utilise the time-series properties of the real estate return series. The third
methodology is a VAR model that allows the testing of the role of the term structure of
interest rates and the gilt-equity yield ratio in forecasting real estate returns. Forecasts
were produced for one to six months ahead and evaluated on the basis of standard
forecast evaluation criteria.
This investigation has found that a vector autoregressive model, incorporating lagged
values of term structure of interest rates and the gilt-equity yield ratio, provides superior
one step (month) ahead predictions of real estate returns than other simpler univariate and
naive forecasting models. However, at longer predictive horizons (that is up to six
months), the relative advantage of the more complex multivariate model for forecasting
equity-based returns disappears. The implication of this finding is that the multivariate
asset pricing models developed in existing work to explain the intertemporal variation in
real estate returns may only be suitable for immediate or short-term forecasts (one to two
steps ahead). The recommendation in the present paper is that analysts can do no better
than to forecast the long term behaviour of indirect, equity-based real estate returns series
based on its long term mean. The short run variation around the mean can be forecast
using multi-factor frameworks. Meanwhile, returns to direct property investments appear
prima facie to be forecastable using time series models at least 6 periods into the future.
17
In the case of indirect property returns, such short-term forecasts can be turned into a
trading rule that can generate excess returns over a buy-and-hold strategy gross of
transactions costs, although none of the trading rules we develop could cover the
associated transactions costs. We therefore conclude that such forecastability is entirely
consistent with stock market efficiency.
18
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movement with other assets, Journal of Real Estate Finance and Economics 5, 401-18.
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9(3), 5-32.
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Thomson Business Press, London.
19
Table 1. Summary Statistics for the Variables 1968-1998
Statistic Indirect Property
Returns
Log-Changes in the
GEYR
Log-Term Spread
Mean 0.869 -0.814 1.182
Variance 64.720 0.015 5.000
Skewness -0.659** -0.061 -0.233
Excess Kurtosis 5.048** 1.174** 0.0346
Minimum -43.905 -1.199 -4.820
Maximum 38.869 -0.3512 6.730
Bera-Jarque 408.226** 20.909** 3.280
Acf(1) 0.125** 0.873** 0.960**
Acf(2) -0.099 0.752** 0.923**
Acf(3) -0.027 0.670** 0.883**
Acf(4) -0.022 0.562** 0.845**
Acf(5) -0.071 0.479** 0.810**
LB-Q*(12) 11.957 1063.998 1650.394**
Notes: Bera-Jarque is a normality test statistic, asymptotically distributed as a 2(2) under the null; Acf(x)
denotes the autocorrelation coefficient at lag x; * and ** denote significance at the 5% and 1% levels
respectively; LB-Q*(12) denotes the Ljung-Box statistic for autocorrelation of order up to 12, which is
distributed asymptotically as a 2(12) under the null.
Table 2. Granger Causality Tests for VAR(4)
Causality from (independent variable)
Indirect Property Index GEYR Term Spread
Causality to Indirect Property Index 0.0232 0.0193 0.0957
(Dependent GEYR 0.4954 0.0000 0.2978
Variable) Term Spread 0.5144 0.1154 0.0000
Note: Cell entries are p-values.
20
Table 3. Out of sample forecast accuracies for indirect (DS) property return
forecasting models 1968 - 1998
Steps Forecasts using
Long term mean ARMA(4,2) ARMA(1,1) ARMA(1,3) VAR(1) VAR(4)
Panel A: Mean Square Error
1 98.9625 143.8746 100.6335 100.7223 99.6245 114.0778
6 98.8341 153.9693 100.8244 100.6871 102.4357 109.0905
Panel B: Mean Absolute Error
1 7.2197 7.1819 7.3820 7.3307 7.2049 7.5951
6 7.2197 7.8485 7.3590 7.3500 7.3528 7.3528
Panel C: % Correct sign predictions
1 58.09 51.86 55.62 57.50 56.88 58.25
6 58.13 46.88 50.00 48.13 55.62 52.50
Table 4. Out of sample forecast accuracies for indirect (DS) property return
forecasting models 1986-1998
Steps Forecasts using
Long term mean ARMA(2,5) VAR(1)
Panel A: Mean Square Error
1 56.8638 76.0518 55.5625
6 56.8842 72.9506 46.4988
Panel B: Mean Absolute Error
1 5.8497 6.9969 5.7702
6 5.8521 6.6779 5.5091
Panel C: % Correct sign predictions
1 58.11 51.35 59.46
6 58.11 51.35 50.00
21
Table 5. Out of sample forecast accuracies for direct (IPD) property return
forecasting models 1986-1998
Steps Forecasts using
Long term
mean
ARMA(4,2) ARMA(1,1) ARMA(1,3) VAR(1) VAR(2)
Panel A: Mean Square Error
1 0.6717 0.2381 0.1729 0.1756 0.7052 0.7061
6 0.6724 0.8661 0.2668 0.2739 0.8917 0.9332
Panel B: Mean Absolute Error
1 0.5459 0.3598 0.2808 0.2999 0.6338 0.6527
6 0.5456 0.6212 0.3556 0.1766 0.7447 0.7677
Panel C: % Correct sign predictions
1 93.24 87.84 91.89 90.54 94.60 91.89
6 91.89 75.68 91.89 90.54 89.49 85.14
Table 6: Profitability of Indirect Property Index Trading Rules based on Out of
Sample Forecasts
Steps ahead
forecasts produced
for:
Trade when forecast next
return > 0.87% per month
Trade when forecast next return
positive
Number of
trades
Average
annual return
Number of
trades
Average
annual return
ARMA(1,3)
1 step ahead 23 2.69% 74 7.91%
6 steps ahead 1 2.95% 68 6.19%
ARMA(1,1)
1 step ahead 22 4.13% 66 8.93%
6 steps ahead 1 2.50% 76 1.87%
ARMA(4,2)
1 step ahead 48 4.55% 77 7.48%
6 steps ahead 34 8.50% 79 5.18%
VAR(4)
1 step ahead 37 7.82% 50 9.26%
6 steps ahead 34 2.28% 51 4.99%
VAR(1)
1 step ahead 37 8.70% 41 9.11%
6 steps ahead 56 3.50% 41 4.93%
Buy and hold equities 1 8.07%
Buy and hold treasury bills 1 2.50%
22
Figure 1: Impulse Responses and Standard Error Bands for
Innovations in the Property Index
-2
0
2
4
6
8
10
1 2 3 4 5 6 7 8 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Steps Ahead
Figure 2: Impulse Responses and Standard Error Bands for
Innovations in the GEYR
-1.5
-1
-0.5
0
0.5
1
1.5
1 3 5 7 9
11
13
15
17
19
21
23
Steps Ahead
23
Figure 3: Impulse Responses and Standard Error Bands for
Innovations in the Term Spread
-1.5
-1
-0.5
0
0.5
1
1 2 3 4 5 6 7 8 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Steps Ahead